ABSTRACT: In this talk we discuss how to understand the tangent cones of Hermitian-Yang-Mills connections in terms of the local algebraic data on the underlying reflexive sheaf. (Joint work with Xuemiao Chen)

ABSTRACT: I will talk about joint work with Hans-Joachim Hein on the conical behavior of Ricci-flat metrics on Calabi-Yau varieties with certain types of isolated singularities. Interesting examples include hypersurfaces with nodal singularities. In the more technical part I will try to sketch the main steps involved in the proof.
January 10:

September 9, 2016
TITLE: Degeneration of Calabi-Yau metrics

ABSTRACT: The complex structure moduli space of Calabi-Yau manifolds can be compactified using the Gromov-Haudorff topology, and a central question is to understand the structure of these Gromov-Hausdorff limits. We will focus on the “non-collapsing” case, and explain the connection with algebraic geometry (joint work with S. Donaldson), and the recent example of a compact Calabi-Yau manifold with isolated conical singularities (joint work with H. Hein). A well-known application of the latter is the existence of special Lagrangian spheres on the smoothing of nodal Calabi-Yau varieties.